Simultaneous Pit and Waste Dump Schedule Optimization

Transcription

1 Simultaneous Pit and Waste Dump Schedule Optimization Jim Butler Minemax, Inc. Tim George Metal Mining Consultants, Inc. SME Annual Meeting, Denver Technology: Mine Planning and Optimization Session February 26, 2013

2 Overview Current Practice in Pit and Detailed Waste Dump Scheduling Problems with Current Practice Formulation for Joint Pit and Detailed Waste Dump Scheduling Examples (igantt, Tempo, Minemax Scheduler) Extensions (Multiple Waste Dumps, Heap Leach, Reactive Waste) Conclusion

3 Current Practice Develop Mine (Pit) Schedule with Rough Consideration of Waste Movements Adjust Total Material Movement Limit Compute Detailed Waste Dumping Sequence Analyse Trucking Utilization vs Availability Determine Trucking Requirements

4 Accounting for Waste in Mining Schedule Basic Approach : Account for waste movement and dumping only through total material movement expressed in tonnes. Advanced Approach: Consider pit depth dependent trucking requirements on a per block basis

5 Waste Accounting Basic Approach Total Material Movement upper limit can be based on digging and/or hauling capability in tonnes per period. However, trucking requirements for a given tonnage to be mined can actually vary depending on where the material is mined from. Basic approach does not account for trucking requirements which vary with depth of mined block in the pit. Trucking requirements for waste can vary depending on where it is placed on the waste dump. Does not account for trucking requirements associated with detailed waste dumping.

6 Waste Accounting Advanced Approach Based on cycle-times and truck capacities, model truckhours and set a limit on available truck hours. Accounts for depth dependent trucking requirements for ore out of pit and to crusher. Accounts for depth dependent trucking requirements for waste out of pit but not to final resting place in waste dump.

7 Waste Accounting Advanced Approach: Centroid Problem May use waste dump centroid as average distance for waste. Results in over-estimating or under-estimating real trucking requirements. With over-estimating there can be a loss in value With under-estimating, the schedule is impractical

8 Pieces of the Puzzle for Proposed Formulation Financials Based on Trucking Model Individual Waste Dump Blocks Trucking for Pit and Waste Dump Precedences Between Waste Dump Blocks Volume Balance Constraints

9 Linear Programming Context for Scheduling LP formulation can be viewed as a matrix with columns as decision variables and rows as constraints using decision variables In mine scheduling, use proportion of block to be mined in a period as decision variable : B ij is a variable with a range between 0 and 1 representing the proportion of block i mined in period j Blocks can have multiple quantities associated with them e.g. Mill tonnes, Mining tonnes, Metal Tonnes denote Q ik as the k th quantity in block i For each quantity and in each time period, we can specify minimum and/or maximum total quantities denoted by row names of QC kj indicating total quantity k in period j

10 Linear Programming Matrix General Form B11 B12 B13 B14 B21 B22 B23 B24... v v v v v v v v QC11 Q11 Q21 QMAX11 QC12 Q11 Q21 QMax12 QC13 Q11 Q21 QMAX13 QC14 Q11 Q21 QMAX14 QC21 Q12 Q22 QMAX21 QC22 Q12 Q22 QMAX22 QC23 Q12 Q22 QMAX23 QC24 Q12 Q22 QMAX24 QMIN jk BijQik QMAX i jk

11 LPMatrix: Mining and Milling Example B11 B12 B13 B14 B21 B22 B23 B , , ,000 60,000-5,000-4,700-4,200-3,500 Mill ,000,000 Mill ,000,000 Mill ,000,000 Mill ,000,000 Mine ,000,000 Mine ,000,000 Mine ,000,000 Mine ,000,000 B1 is 2500 tonnes of ore B2 is 2500 tonnes of waste

12 Model Individual Waste Dump Blocks A waste dump is divided into a number of horizontal lifts. Lifts are further divided into dump blocks. Include waste dump blocks into the LP similar to pit blocks

13 Precedences Between Waste Dump Cells Define precedences between waste dump blocks corresponding to practical waste dump construction

14 Detailed Waste Dump Modelling for Scheduling Introduce waste dump volume (wdv) as a positive quantity for waste dump blocks and a negative quantity for pit blocks Specify wdv balance constraints for each period. i BijQik 0 Where k is the waste dump volume quantity

15 Detailed Waste Dump Modelling: Trucking Pit blocks use cycle times to calculate required truck hours to a common point of passage enroute to the waste dump Waste dump blocks use cycle times to calculate required truck hours from the common point of passage to the waste dump block Specify truck hours availability constraints for each period. i B ij Q ik QMAX k Where k is the truck hours quantity Assign a cost/hour to trucking

16 Examples Modelling approach can be applied to any lpbased mine scheduling solution which supports blocks with multiple quantities and constraints Example 1: igantt Example 2: Minemax Scheduler Example 3: Tempo

17 igantt Example: Activity Types LoadHaul and WasteDumping as Activity Types

18 igantt Example: DumpVol Quantity DumpVol Quantity LoadHaul takes ve values WasteDumping takes +ve values

19 igantt Example: DumpVol Constraint Total DumpVol balance set to be exactly zero (-ve from LoadHaul, +ve from WasteDumping)

20 igantt Example: Activities in Gantt Chart

21 Minemax Scheduler Example

22 Minemax Scheduler: DumpVol Constraint

23 Minemax Scheduler: DumpVol Report

24 Minemax Scheduler: 3D by Time

25 Tempo Example

26 Tempo Example : Dump Constraints Dump volume balance constraint included together with processing constraints Trucking requirements dependent upon detailed dump location

27 Tempo Example : Dump Results Volume of sub-grade and waste classification material from pit balances with waste volume provided from dump

28 Multiple Waste Dumps Any number of waste dumps (e.g. short haul, long haul) can be set up Each waste dump uses a common waste dump volume quantity Single multi-period optimization will choose alternative waste dumps to balance trucking over life of mine

29 Heap Leach Introduce a heap leach dump volume quantity in addition to the heap leach ore tonnes quantity Define heap leach locations as lifts or blocks similar to a waste dump Heap leach locations contribute to heap leach dump volume quantity Blocks scheduled to heap leach contribute to both heap leach ore quantity and heap leach dump volume quantity Define volume balance constraints for heap leach dump volume quantity

30 Containing Reactive Waste Introduce reactive and non-reactive wdv quantities which each have their own volume balance constraints Internal dump blocks and in-pit reactive waste blocks contribute to reactive wdv quantity External dump blocks and in-pit non-reactive waste blocks contribute to non-reactive wdv quantity

31 Conclusion Introduced a generic way to model joint pit and detailed waste dump schedule optimization Implemented modelling technique in 3 of Minemax s schedule optimization solutions Outlined extensions for multiple waste dumps, heap leach and reactive waste Modelling technique can be applied to any lp-based mine schedule optimizer that models multiple quantities on a block